deep-ei 0.5.0

Tools for examining the causal structure of artificial neural networks built with PyTorch

deep-ei

This package accompanies the paper "Examining the Causal Structures of Artificial Neural Networks Using Information Theory" by Simon Mattsson, Eric J. Michaud, and Erik Hoel

What's here?

This repository contains all the code used in the paper (notebooks for creating figures, experiment scripts, etc) in the experiments directory, but most importantly holds the open-source deep-ei module. We encourage people to install deep-ei and perform their own experiments on new datasets, neural network architectures, etc. There are so many experiments we'd like to do, but haven't had time to yet! If you'd like to contribute to code, just submit a pull request! (note that all the code is currently structured as a single module, but may eventually be restructured as a package if that makes sense).

Installation:

The simplest way to install the deep_ei module is with:

pip install deep-ei

The simplest way to install the deep_ei module is simply to navigate to this directory and execute:

pip install .

An Anaconda environment has also been provided, so you can create a new Anaconda environment with this module and its dependencies simply with:

conda env create --file environment.yml

Since it is recommended that PyTorch be installed with Anaconda, for many it will be easiest to install pytorch first with conda install -c pytorch pytorch, and then execute pip install ., which will then install the other dependencies (scikit-learn, fast_histogram) and install the deep_ei module itself.

Some basic tests have been included, which you can run using:

python setup.py test

Usage:

import torch
import torch.nn as nn

from deep_ei import topology_of, ei_of_layer

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
dtype = torch.float32
torch.set_default_dtype(dtype)

network = nn.Linear(10, 10, bias=False).to(device)
top = topology_of(network, input=torch.zeros((1, 10)).to(device))

EI = ei_of_layer(network, top,
                    threshold=0.05,
                    batch_size=100, 
                    in_range=(0, 1),
                    in_bins=64,
                    out_range=(0, 1),
                    out_bins=64,
                    activation=nn.Sigmoid(), 
                    device=device)

Which will compute the EI of our network using a sigmoid activation. By default, this function will increase the number of samples it uses until the EI levels off (characterized by whether it will change by more than threshold of its current value even if we doubled the number of samples).

Using the data from the topology_of function, it can infer activation function and input and output ranges:

network = nn.Sequential(
    nn.Linear(20, 10, bias=False),
    nn.Sigmoid(),
    nn.Linear(10, 5, bias=False),
    nn.Tanh()
)
top = topology_of(network, input=torch.zeros((1, 20)).to(device))

layer1, _, layer2, _ = network

EI_layer1 = ei_of_layer(layer1, top,
                    threshold=0.05,
                    batch_size=100, 
                    in_range=(0, 1),
                    in_bins=64,
                    out_bins=64, 
                    device=device)

EI_layer2 = ei_of_layer(layer2, top,
                    threshold=0.05,
                    batch_size=100, 
                    in_bins=64,
                    out_bins=64, 
                    device=device)

Which will use an activation of nn.Sigmoid and an out_range of (0, 1) for the first layer and an activation of nn.Tanh and an out_range of (-1, 1) for the second layer. Note that we have to specify an in_range for the first layer.

Instead of specifying a threshold, you can instead manually specify a number of samples to use when computing effective information:

network = nn.Linear(10, 10, bias=False).to(device)
top = topology_of(network, input=torch.zeros((1, 10)).to(device))

EI = ei_of_layer(network, top,
                    samles=50000,
                    batch_size=100, 
                    in_range=(0, 1),
                    in_bins=64,
                    out_range=(0, 1),
                    out_bins=64,
                    activation=nn.Sigmoid(), 
                    device=device)

You can also measure the sensitivity of a layer like so:

network = nn.Linear(10, 10, bias=False).to(device)
top = topology_of(network, input=torch.zeros((1, 10)).to(device))

sensitivity = sensitivity_of_layer(network, top,
                            samples=1000,
                            batch_size=100, 
                            in_range=(0, 1),
                            in_bins=64,
                            out_range=(0, 1),
                            out_bins=64,
                            activation=nn.Sigmoid(), 
                            device=device)